Tabulation of cubic function fields with imaginary and unusual Hessian

  • Authors:

  • Pieter Rozenhart;Renate Scheidler

  • Affiliations:

  • Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada;Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada

  • Venue:
  • ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
  • Year:
  • 2008

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Abstract

We give a general method for tabulating all cubic functionfields over Fq(t) whose discriminant D has odd degree, or even degreesuch that the leading coefficient of -3D is a non-square in Fq*, up toa given bound on |D| = qdeg(D). The main theoretical ingredient is ageneralization of a theorem of Davenport and Heilbronn to cubic functionfields. We present numerical data for cubic function fields over F5 andover F7 with deg(D) ≤ 7 and deg(D) odd in both cases.